System and method for optimizing an aircraft trajectory

ABSTRACT

Systems and methods of the present invention are provided to generate a plurality of flight trajectories that do not conflict with other aircraft in a local area. Interventions by an air traffic control system help prevent collisions between aircraft, but these interventions can also cause an aircraft to substantially deviate from the pilot&#39;s intended flight trajectory, which burns fuels, wastes time, etc. Systems and methods of the present invention can assign a standard avoidance interval to other aircraft in the area such that a pilot&#39;s aircraft does not receive an intervention by an air traffic control system. Systems and methods of the present invention also generate a plurality of conflict-free flight trajectories such that a pilot or an automated system may select the most desirable flight trajectory for fuel efficiency, speed, and other operational considerations, etc.

CROSS REFERENCE TO RELATED APPLICATION

This application is a Continuation of U.S. application Ser. No.14/949,529 filed Nov. 23, 2015, which claims priority to U.S.Provisional Patent Application Ser. No. 62/191,573 filed Jul. 13, 2015,the disclosures of which are incorporated herein in their entireties byreference.

FIELD OF THE INVENTION

The present invention relates to the systems and methods for generatingflight trajectories for aircraft in flight to meet operationalrequirements, minimize fuel burn, reduce off path vectoring, andminimize the number of level flight segments during climbs and descents.

BACKGROUND OF THE INVENTION

The Federal Aviation Administration (FAA) and other Air NavigationService Providers (ANSPs) around the world maintain air traffic controlsystems (ATCs) to organize the flow of aircraft traffic in a particularairspace and to avoid conflicts and prevent collisions among airborneaircraft. To accomplish this task, ATCs rely on ground-based radarsystems to determine the “state vector” of an aircraft which includesaltitude, position, East-West velocity, North-South velocity, andvertical rate. Currently, ATCs use these state vectors to coordinate theflow of aircraft traffic, and ATCs maintain spacing between aircraft bydictating instructions to individual aircraft. However, individualaircraft do not receive the radar based state vector of other aircraftin the area, and aircraft rely on ATC to provide instructions that avoidconflicts and possible collisions with other aircraft.

ATCs are required to intervene and assign an aircraft a different speed,a level segment, or an off course vector if two aircraft are on flightpaths that conflict. In some cases, ATCs will assign all three tomaintain proper separation between aircraft. These interventions alsoadd workload for the ATCs, increase fuel burn, cause excess carbondioxide and nitric oxide emissions, and can increase noise levelsexperienced by the surrounding community.

In addition, pilots plan a phase of flight trajectories withoutknowledge of other aircraft in the area, and interventions by ATCsdisrupt these plans. For example, when planning the descent phase of theflight, the pilot selects the desired descent speeds and determines theTop of Descent (TOD), which is the aircraft's transition between the enroute phase and the descent phase of the flight. The pilot selects thedesired descent speeds based on operational requirements such asmaximizing fuel efficiency, improving the arrival time of the aircraft,or other parameters, such as turbulence avoidance, that characterize theflight trajectory. These operational requirements may be derived from apilot flying the aircraft or the Airline Operations Control (AOC) thatcoordinates aircraft for an airline company. The operational limits usedin determining the descent speeds can be set by the manufacturer, theaircraft operator, and the government regulators that oversee theoperation of aircraft. On aircraft equipped with a Flight ManagementSystem (FMS) which automates certain in-flight tasks, the operationalrequirement may be set within the FMS to reduce cost or improve fuelefficiency. Prior to the TOD the pilot selects the appropriate speedprofile within the FMS to plan a descent phase for the aircraft that,for example, minimizes fuel burn. In other instances, the operationalrequirement may be to fly faster and arrive at an airport to meet ascheduled arrival time. These operational requirements are inhibited andsometimes vitiated when an ATC intervenes during an aircraft's decentphase.

To supplement state vector information from ground-based radar systems,the aviation industry is developing and deploying the AutomaticDependent Surveillance-Broadcast (ADS-B) system, which requires anaircraft to broadcast state vector information determined by theaircraft's onboard sensors. The FFA defines the capabilities of ADS-Bunder the DO-260B standard. This change enables other aircraft in thearea to receive the broadcasted ADS-B data and the state vector of otherproximate aircraft. Now, aircraft are able to receive state vectorinformation directly from other aircraft instead of solely relying onthe ATC to provide instructions and avoid conflicts and possiblecollisions with other aircraft.

Even with knowledge of aircraft in the area, current trajectorygenerating devices are inflexible. These devices provide a pilot witheither a single proposed trajectory that identifies the trajectory ofminimum fuel burned or a single proposed trajectory that identifies theleast amount of time required to fly the proposed trajectory. Thesetrajectory solutions are limited to cruise flight that are accomplishedby adjusting the speed, the vertical and/or the horizontal paths of thetrajectory. When the devices provide single, automated solutions in thisfashion, they remove the pilot and other entities from the decisionmaking process and do not allow for more comprehensive, efficientsolutions to be identified. While pilots can plan flight trajectoriesthat best suit one operational requirement, pilots still rely on ATCs toensure safe separation between aircraft.

In addition, pilots lack state vector information of surroundingaircraft, but pilots may also lack additional information includingup-to-date wind information, special use airspace, turbulenceinformation, volcanic ash reports, ANSP sector boundaries, letters ofagreement between ANSP sectors, ATC sector loading, country over flightcosts, temperature inversion layers, sonic boom regulations, thetransport of wake vortices and sonic booms. Therefore, there is a needfor a system and a method that generates a plurality of flighttrajectories that synthesizes information from multiple sources andprevents or minimizes interventions by ATCs, which undermine theoperational requirements associated with the aircraft.

SUMMARY OF THE INVENTION

In accordance with the invention, systems and methods are provided forgenerating a plurality of conflict-free flight trajectories that bestsuits one or more selected operational requirements of a pilot, an AOC,an ATC, etc. The plurality of conflict-free flight trajectories providemore than separation assurance from other aircraft. The plurality offlight trajectories is free of conflicts such as other aircraft, weatherevents, no-fly zones, and other restrictions. In addition, theconflict-free flight trajectories are vetted or calculated based on oneor more parameters. For example, flight trajectories may be generatedbased on fuel efficiency, time efficiency, optimum airspeed, andcombinations of the same. The resulting plurality of conflict-freeflight trajectories saves fuel and time, offers flexibility to pilotsand airlines, reduces the workload of ATCs, reduces fuel burn, reducesnoise, reduces the emission of carbon dioxide, and reduces nitric oxideby requiring fewer interventions.

The system for generating a plurality of conflict-free flighttrajectories may generate a first set of flight trajectories based on afirst parameter and a second set of flight trajectories based on asecond parameter. For example, the first set of flight trajectories maybe generated by first calculating the most fuel efficient flighttrajectory, i.e., the flight trajectory that burns the least amount offuel. For the next iteration, the first solution is suppressed, and thesecond-most fuel efficient flight trajectory is calculated. Thisiterative process continues until a flight trajectory is calculated thatconsumes the maximum incremental amount of fuel allowable, which may beestablished by a pilot, an airline, a government regulation, etc. Asimilar iterative process generates a second set of flight trajectoriesbased on time. A subsequent post-processing method may be applied to thetwo sets of flight trajectories, including various set operations thatconstruct new sets of flight trajectories from the two sets of flighttrajectories. These set operations include “union,” which adds thecontents of both sets, or in other words, the union of two sets is theset of all flight trajectories in both sets. The set operation of“intersection” creates a new set with only the flight trajectories thatare present in both the first set and the second set. In the setoperation of “set difference,” a new set is created that has all of theflight trajectories in the first set that are not present in the secondset. With the set operation of “symmetric difference,” a new set offlight trajectories is created that has all of the flight trajectoriesin the first set that are not present in the second set, all of theflight trajectories in the second set that are not present in the firstset, but none of the flight trajectories that are in both the first setand the second set. It will be appreciated that these embodiments mayinclude other set operations and/or additional sets of flighttrajectories based on additional parameters. Once the post-processing iscomplete, the resulting set of flight trajectories may be presented to apilot so that the pilot may select a flight trajectory or input into analgorithm that automatically selects a flight trajectory. In someembodiments, once the flight trajectory is selected a new TOD isgenerated and entered into the FMS.

In another aspect of the invention, a standard avoidance interval (SAI)is assigned to proximate aircraft to prevent interventions by ATCs. ASAI is an enclosed volume, or partially enclosed volume, that theinstant aircraft assigns to other aircraft in the area. The SAIfunctions as a spatial buffer between the instant aircraft and the otheraircraft in the area. For example, if the instant aircraft determines aflight trajectory that passes within the SAI assigned to anotheraircraft, then there is a conflict because the instant aircraft ispassing too close to the other aircraft. In the United States, FAAguidelines dictate when two aircraft are too close together and when anATC intervenes to change the spacing between two aircraft. Therefore,the instant aircraft assigns a SAI to other aircraft that is larger, ormore conservative, than FAA guidelines. By not conflicting with theassigned SAI, the instant aircraft comports with FAA guidelines andavoids interventions by ATCs.

In an exemplary embodiment, the enclosed volume of the SAI has acylinder shape defined by a vertical separation distance extending aboveand below the aircraft and defined by a constant horizontal radiusextending from a vertical axis of the aircraft. The size and shape ofthe SAI assigned to a local aircraft may depend on the speed,performance, size, configuration and type of aircraft, the proximity toan ATC boundary or airport, the point in the flight trajectory, etc.Further, different entities may use their own SAI standards. Forexample, SAI standards may be established by an airline, an aircraftoperator, an airport, a Metroplex of airports, an airspace sector, anational airspace system or an international standard defined by theInternational Civil Aviation Organization (ICAO). It will be appreciatedthat in some embodiments of the present invention, a SAI may be assignedto another aircraft that dictates the maximum distance between twoaircraft instead of how close two aircraft may be separated. Thus, anaircraft may have more than one SAI.

Once a SAI has been assigned to a local aircraft, a miss distance can becalculated and compared to the SAI to determine if there is a conflict,i.e., a potential collision or close call. The miss distance is theclosest distance that two aircraft will pass relative to each other, andin some embodiments, the miss distance is a vector with directionalinformation. The miss distance is calculated based on the state vectorinformation of both aircraft. While information such as position, speed,direction, and vertical climb/descent rate are useful when calculating amiss distance, these parameters may not prove useful in specificinstances, for example, when a local aircraft makes a banking turn orotherwise changes its path. Therefore, it is contemplated in someembodiments, that a rate change or acceleration of the bearing or one orboth of the relevant aircraft may be utilized to provide a more accuratedetermination of a miss distance. Further, information such as a meterfix or a way point, which are reference points in space that an aircraftpasses through, and a destination may be accounted for when determininga miss distance. The miss distance is then compared to the SAI of thelocal aircraft. If the miss distance places the instant aircraft withinthe SAI of the local aircraft, then there is a conflict, and theproposed flight trajectory is not conflict free. Once the SAI and themiss distance determine which flight trajectories are conflict free, aFMS may update the TOD for a descent phase of the flight.

A flight trajectory may pass through a traffic avoidance waypoint (TAW)to avoid a conflict with a local aircraft. In one example, an instantaircraft has established a flight trajectory between a TOD and awaypoint close to an airport, but the SAI of a local aircraft and themiss distance between the two aircraft causes a conflict. Several TAWsare provided that have a sufficiently large miss distance and areconflict free. The pilot of the instant aircraft may then select a TAWfor the aircraft to travel through that best suits the relevantoperational requirements, and a new flight trajectory and a new TOD maybe subsequently determined. The new flight trajectory may be curved andmay pass through the selected TAW point in some embodiments. In anexemplary embodiment, a brachistochronic flight trajectory, which is thetrajectory of fastest descent between the TOD and the end of the chosendescent segment, is chosen to pass through the selected TAW point.Alternatively, in other embodiments, the flight path is discretized intosegments with separate constant speed profiles, and the selected TAWserves as a transition point between segments.

It will be appreciated that the plurality of TAWs may be onedimensional, two dimensional, or three dimensional. In the onedimensional embodiment, the TAWs are located at various altitudes over areference point on the ground path, and thus the TAWs form a verticalpath along the instant aircraft's flight plan path. In an exemplary twodimensional embodiment, multiple TAWs may form a two dimensional area,and the multiple TAWs are positioned over different locations along theground path. Lastly, in the three dimensional embodiment, multiple TAWsmay form a three dimensional body, and some TAWs may not be positionedover the flight plan ground path.

In further embodiments, the TAWs are limited, for example, in view of aconflict like a local aircraft that is too close to an instant aircraft.In some embodiments, an upper altitude limit, a lower altitude limit, anupper speed limit, and/or a lower speed limit govern which TAWs areconflict free. Once a TAW is selected, a new flight trajectory iscalculated.

Embodiments of the present invention may generate other waypoints that,either alone or in combination with the TAWs, allow a flight trajectoryto be optimized for other factors. For example, a flight trajectory maypass through an energy management waypoint (EMW) to achieve a desiredtotal energy state at a desired location over the ground. In oneembodiment, an instant aircraft has established a conflict free flighttrajectory comprised of several TAWs that have a sufficiently large missdistance between the TOD and the desired landing runway. By selecting alanding function an additional EMW is inserted into the trajectory toensure that the aircraft's total energy state is compatible with makinga safe final approach and landing on the desired runway. The landingfunction may generate EMWs in addition to the conflict free TAWs, inwhich case the flight trajectory passes through the selected TAW and theselected EMW. In some embodiments, one or more EMWs are selected fromthe conflict free TAWs, and the selected TAW and the selected EMW mayconstitute the same waypoint. Further still, a plurality of TAWs and aplurality of EMWs are generated where the two sets of waypointspartially overlap.

Another example of an EMW is when the pilot wishes to avoid spendingtime at an altitude (or range of altitudes) where aircraft structuralicing occurs. By inserting EMWs into the trajectory the instant aircraftcould avoid spending time at altitudes where icing conditions exist. Inyet another example the aircraft's total energy could be managed toavoid possible injury to passengers and crew by being within the optimumspeed for penetration of turbulent airspace. By inserting EMWs into thetrajectory the instant aircraft can travel at the proper speed forturbulent conditions and avoid excessively violent gyrations associatedwith flying too fast in turbulent air.

It will be appreciated that EMWs can be used when there is no trafficand that EMWs could also be generated and selected in combination with aTAW when traffic is present. It will further be appreciated that whenEMWs are inserted into the planned trajectory prior to the TOD the FMScan then optimize the entire trajectory of standard waypoints, TAWs andEMWs.

Considering the above described features and attributes, in one aspectof the invention, it can be considered a method for automaticallydetermining a plurality of conflict-free flight trajectories for a firstaircraft, comprising: (i) providing at least one electronic device toprocess instructions for determining a plurality of flight trajectories;(ii) providing information regarding a first aircraft moving in spaceaccording to a state vector; (iii) providing information regarding asecond aircraft moving in space according to a state vector, the secondaircraft having a standard avoidance interval extending in at least onedirection from the second aircraft; (iv) determining, by the at leastone electronic device, a first flight trajectory for the first aircraftbased on the state vector of the first aircraft, the first flighttrajectory being optimized for a first parameter; (v) comparing, by theat least one electronic device, the first flight trajectory to the statevector of the second aircraft to determine a miss distance between thefirst aircraft and the second aircraft; (vi) comparing, by the at leastone electronic device, the miss distance to the standard avoidanceinterval of the second aircraft to confirm that the miss distance isgreater than the standard avoidance interval; (vii) determining, by theat least one electronic device, a second flight trajectory for the firstaircraft based on the state vector of the first aircraft, the secondflight trajectory being distinct from the first flight trajectory; and(viii) sending instructions to the first aircraft indicating the firstand second flight trajectories, and wherein the first aircraft travelson a flight trajectory from one of the first and second flighttrajectories.

In various aspects of the invention, it may be considered a method,further comprising comparing, by the at least one electronic device, thesecond flight trajectory to the state vector of the second aircraft todetermine a second miss distance between the first aircraft and thesecond aircraft; and comparing, by the at least one electronic device,the second miss distance to the standard avoidance interval of thesecond aircraft to confirm that the second miss distance is greater thanthe standard avoidance interval. The first flight trajectory may beoptimized for fuel or time efficiency, wherein a plurality of flighttrajectories range between the first flight trajectory and a flighttrajectory that uses the maximum incremental fuel or time allowance.

In another aspect of the invention, it can be considered a method forautomatically determining a plurality of traffic avoidance waypoints forconflict-free flight trajectories for a first aircraft, comprising: (i)providing at least one electronic device to process instructions fordetermining a plurality of traffic avoidance waypoints; (ii) providinginformation regarding a first aircraft moving in space according to astate vector; (iii) providing information regarding a second aircraftmoving in space according to a state vector, the second aircraft havinga standard avoidance interval extending in at least one direction fromthe second aircraft; (iv) determining, by the at least one electronicdevice, a first flight trajectory for the first aircraft based on thestate vector of the first aircraft, the first flight trajectory having aground path; (v) comparing, by the at least one electronic device, thefirst flight trajectory to the state vector of the second aircraft todetermine a miss distance between the first aircraft and the secondaircraft when the first aircraft is located at a miss point on the firstflight trajectory, wherein the standard avoidance interval of the secondaircraft is greater than the miss distance, and wherein a referencepoint is located on the ground path of the first flight trajectory belowthe miss point; (vi) determining, by the at least one electronic device,a plurality of traffic avoidance waypoints at various altitudes abovethe reference point, wherein each traffic avoidance waypoint has a missdistance relative to the state vector of the second aircraft that islarger than the standard avoidance interval of the second aircraft; and(vii) selecting a traffic avoidance waypoint from the plurality oftraffic avoidance waypoints based on at least one parameter, and whereinthe first aircraft travels through the selected traffic avoidancewaypoint.

In some aspects, it can be considered a system further comprising (viii)providing information regarding an icing event having a volume; (ix)determining, by the at least one electronic device, a plurality ofenergy management waypoints at various altitudes above the ground pathof the first flight trajectory, wherein the plurality of energymanagement waypoints avoid the volume of the icing event; and (x)selecting an energy management waypoint from the plurality energymanagement waypoints, wherein the first aircraft travels through theselected energy management waypoint. In some embodiments, at least aportion of the volume of the icing event has a temperature between −5°C. and 2° C. In various embodiments, the plurality of energy managementwaypoints at least partially overlaps with the plurality of trafficavoidance waypoints.

In further aspects, it can be considered a system further comprising(viii) providing information regarding a turbulence event having avolume; (ix) determining, by the at least one electronic device, aplurality of energy management waypoints at various altitudes above theground path of the first flight trajectory, wherein the plurality ofenergy management waypoints avoid the volume of the turbulence event;and (x) selecting an energy management waypoint from the pluralityenergy management waypoints, wherein the first aircraft travels throughthe selected energy management waypoint. In some embodiments, at least aportion of the turbulence event has a Reynolds Number greater than 5000.

In another aspect of the invention, it can be considered a system forautomatically determining a plurality of conflict-free trajectories fora first aircraft, comprising: (i) a local data device that determines astate vector for a first aircraft, the local data device sends the statevector for the first aircraft to a trajectory generation device; (ii) atransmitted data device that determines a state vector for a secondaircraft, the transmitted data device sends the state vector for thesecond aircraft to the trajectory generation device; (iii) thetrajectory generation device assigns a standard avoidance interval tothe second aircraft, the standard avoidance interval extends in at leastone direction from the second aircraft, the trajectory generation devicedetermines a plurality of flight trajectories based on the state vectorof the first aircraft, the trajectory generation device compares eachflight trajectory to the state vector of the second aircraft todetermine a plurality of miss distances, the trajectory generationdevice confirms that each miss distance is greater than the standardavoidance interval for the second aircraft; and (iv) a flight managementsystem receives a conflict-free flight trajectory from the plurality ofconflict-free flight trajectories, wherein the flight management systemexecutes the received conflict-free flight trajectory, and the firstaircraft travels on the received conflict-free flight trajectory.

In various aspects, it can be considered a system further comprising adisplay unit operably interconnected to the trajectory generationdevice, the display unit displays the plurality of conflict-free flighttrajectories; and an input user interface operably interconnected to thedisplay unit and the flight management system, the input user interfaceconfigured to receive at least one input in response to the plurality ofconflict-free flight trajectories being displayed on the display unit,the input user interface sends a selected conflict-free flighttrajectory to the flight management system. The at least one receivedinput is one of a physical input from a pilot, and an automated inputfrom a system based on at least one parameter. In some aspects, it canbe considered a system further comprising an onboard traffic device thatis operably interconnected to the transmitted data device and thetrajectory generation device; and an internet-based data device thatdetermines another state vector for the second aircraft, wherein theonboard traffic device synthesizes the state vector for the secondaircraft from both the transmitted data device and the internet-baseddata device, and sends the synthesized state vector for the secondaircraft to the trajectory generation device. In another aspect, it maybe considered a system further comprising an air data device thatgenerates at least one of airspeed data and atmospheric data surroundingthe first aircraft, and the air data device sends the data to thetrajectory generation device.

In another aspect of the invention, it can be considered a system forautomatically determining a plurality of conflict-free trajectories fora first aircraft, comprising: (i) a local data device that determines astate vector for a first aircraft, the local data device sends the statevector for the first aircraft to a trajectory generation device; (ii) atransmitted data device that receives a known flight trajectory of asecond aircraft, the transmitted data device sends the known flighttrajectory of the second aircraft to the trajectory generation device;(iii) the trajectory generation device assigns a standard avoidanceinterval to the second aircraft, the standard avoidance interval extendsin at least one direction from every point along the known flighttrajectory of the second aircraft, the trajectory generation devicedetermines a plurality of flight trajectories based on the trajectory ofthe first aircraft, the trajectory generation device compares eachflight trajectory to the known flight trajectory of the second aircraftto determine a plurality of miss distances, the trajectory generationdevice confirms that each miss distance is greater than the standardavoidance interval for the second aircraft; and (iv) a flight managementsystem receives a conflict-free flight trajectory from the plurality ofconflict-free flight trajectories, wherein the flight management systemexecutes the received conflict-free flight trajectory, and the firstaircraft travels on the received conflict-free flight trajectory.

In yet another aspect of the invention, it can be considered a methodfor automatically determining a plurality of conflict-free flighttrajectories for a first aircraft, comprising: (i) providing at leastone electronic device to process instructions for determining aplurality of flight trajectories; (ii) providing information regarding afirst aircraft moving in space according to a state vector; (iii)providing information regarding a second aircraft moving in spaceaccording to a state vector, the second aircraft having a standardavoidance interval extending in at least one direction from the secondaircraft; (iv) determining, by the at least one electronic device, aplurality of first flight trajectories for the first aircraft based onthe state vector of the first aircraft, the plurality of first flighttrajectories being optimized for a first parameter; (v) comparing, bythe at least one electronic device, a plurality of miss distancesbetween the plurality of first flight trajectories and the state vectorof the second aircraft to the standard avoidance interval of the secondaircraft to confirm that the plurality of miss distances is greater thanthe standard avoidance interval; (vi) determining, by the at least oneelectronic device, a plurality of second flight trajectories for thefirst aircraft based on the state vector of the first aircraft, theplurality of second flight trajectories being optimized for a secondparameter; (vii) comparing, by the at least one electronic device, aplurality of miss distances between the plurality of second flighttrajectories and the state vector of the second aircraft to the standardavoidance interval of the second aircraft to confirm that the pluralityof miss distances is greater than the standard avoidance interval of thesecond aircraft; and (viii) combining, by the at least one electronicdevice, the plurality of first flight trajectories with the plurality ofthe second flight trajectories to form a plurality of conflict-freeflight trajectories. In some aspects, it may be considered combining ofthe plurality of first flight trajectories with the plurality of thesecond flight trajectories is performed by at least one of a unionoperation, an intersection operation, a set difference operation, and asymmetric difference operation.

In yet another aspect of the invention, it can be considered that the amethod for automatically determining a plurality of conflict-free flighttrajectories can reside on the ground or in another aircraft and thentransmitted to the aircraft that will use the plurality of conflict-freeflight trajectories to avoid ATC intervention.

Further advantages and features of the invention will become apparentfrom a review of the following detailed description, taken inconjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference is now made to the following detailed description taken inconjunction with the accompanying drawings in order for a more thoroughunderstanding of the invention.

FIG. 1 illustrates a prior art system where an aircraft is entering adescent phase of a flight trajectory and there are no other aircraft inthe area;

FIG. 2 illustrates a prior art system where an aircraft is entering adescent phase of a flight trajectory toward a merge point where a secondaircraft is also traveling toward the merge point;

FIG. 3 illustrates a prior art system where an aircraft entering adescent phase of a flight trajectory has deviated course on a longvector to avoid encroaching on a second aircraft;

FIG. 4 is a Traffic Avoidance Spacing (TAS) system that generates aplurality of conflict-free flight trajectories;

FIG. 5A is a top plan view of a second aircraft that has been assigned aStandard Avoidance Interval (SAI);

FIG. 5B is a side elevation view of a second aircraft that has beenassigned a SAI;

FIG. 6 shows a first aircraft surrounded by several second aircraft inthe area where the second aircraft have been assigned a SAI;

FIG. 7 is a top plan view of a first aircraft having a state vector anda second aircraft having a state vector where a miss distance betweenthe two aircraft may be calculated using various geometric aspects ofthe respective state vectors;

FIG. 8A illustrates three descent trajectories selected from a pluralityof descent speeds for the descent phase of a flight where the Top ofDescent (TOD) points for different descent trajectories are superimposedon each other and indicate that the various trajectories used in descentcan be used to reach a different point at the end of the chosen descentphase;

FIG. 8B illustrates three descent trajectories selected from a pluralityof descent speeds for the descent phase of a flight where the variousend of descent points of each descent trajectory are superimposed oneach other and indicates that the various trajectories used in descentcan all be used to avoid a second aircraft by the same SAI;

FIG. 9 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory toward a merge point where anotheraircraft that has been assigned a SAI is also traveling toward the mergepoint;

FIG. 10 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory where the aircraft was vectored offcourse for a short distance because the aircraft was not able to fullymeet the assigned SAI and remain on its planned descent path;

FIG. 11 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory toward a merge point where aplurality of SAIs were used, and a single descent trajectory wasselected from a plurality of conflict free descent trajectories thatenables the TAS equipped aircraft to fly a continuous descent;

FIG. 12 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory toward a merge point where aTraffic Avoidance Waypoint (TAW) has been generated and a single descenttrajectory was then selected from a plurality of conflict free descenttrajectories to enable the TAS equipped aircraft to avoid conflicts withmultiple proximate aircraft and fly a continuous descent;

FIG. 13 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory toward a merge point where adifferent TAW has been generated and a single descent trajectory wasthen selected from a plurality of conflict free descent trajectories toenable the TAS equipped aircraft to avoid conflicts with multipleproximate aircraft and fly a continuous descent;

FIG. 14 illustrates an aircraft equipped with a TAS system entering adescent phase of a flight trajectory toward a merge point where adescent trajectory is selected from a plurality of conflict free descenttrajectories to pass through a TAW, which allows the TAS equippedaircraft to fly a continuous descent using a brachistochronic speedprofile passing through the TAW;

FIG. 15 is a top plan view of an aircraft equipped with a TAS systemtraveling along a selected flight trajectory among a plurality ofairways where a series of wind fields are indentified;

FIG. 16 is a top plan view of an aircraft equipped with a TAS systemtraveling along a selected flight trajectory toward a conflict weatherevent where the TAS system has generated an alternative flighttrajectory that is optimized for fuel and another alternative flighttrajectory that is optimized for time;

FIG. 17 is a top plan view of an aircraft equipped with a TAS systemtraveling along a selected flight trajectory toward a conflict weatherevent where the TAS system has generated two sets of flight trajectoriesthat are a plurality of flight trajectories that range between flighttrajectories that are optimized for fuel and time that use a maximumfuel allowance and/or a maximum time allowance;

FIG. 18 is a top plan view of an aircraft equipped with a TAS systemtraveling along a selected flight trajectory where the TAS system hasgenerated a plurality of flight trajectories that use a maximum fuelallowance and/or a maximum time allowance that account for multipleweather events and other operational constraints such as aircraftequipage to operate over water, flight crew qualifications, etc.; and

FIG. 19 illustrates various speed profiles for the descent phase of aflight trajectory.

DETAILED DESCRIPTION

Referring to FIGS. 1-3, several prior art scenarios are provided tohighlight the shortcomings of existing aviation systems that will oftenrequire an air traffic control (ATC) system to intervene and instruct apilot to change the aircraft's flight trajectory. FIG. 1 shows anaircraft 2 that is leaving an en route phase 4 of the aircraft's flighttrajectory and entering a descent phase 6. In this scenario, there areno other aircraft in the immediate area. During the aircraft's en routephase 4, the aircraft 2 is flying at a generally constant altitude.Flight path shadow lines or altitude bars 8 are provided to show therelative altitude of the aircraft's flight trajectory at periodicintervals. The lower ends of the altitude bars 8 create a ground path 10of the flight path that shows where the aircraft 2 is flying above theground.

The transition between the en route phase 4 of the aircraft's flighttrajectory and the descent phase 6 is called the Top of Descent (TOD)12. The TOD 12 is an important aspect of the aircraft's 2 overall flighttrajectory because this is the point where an onboard Flight ManagementSystem (FMS) or pilot can plan the descent phase 6 to be as efficient aspossible with respect to fuel, other costs, time, range, etc., or anycombination thereof. For example, the FMS may set a TOD 12 such that theaircraft 2 glides as long as possible with the engines at idle power toconserve the maximum amount of fuel.

At the end of the decent phase 6, the aircraft 2 enters a low altitudeflight phase 14, which may be defined by the airport and its ATC systemsby a series of waypoints that the aircraft must pass through as theaircraft lands at the airport. In the embodiment shown in FIG. 1, amerge point 16 establishes a transition between the descent phase 6 ofthe aircraft's flight trajectory to the low altitude phase 14. A finalapproach fix 18 aligns the aircraft 2 for its final descent to atouchdown point 20 on the airport's runway 22.

As shown in FIG. 1, there are no other aircraft in the area. Therefore,the airport and its ATC system will not intervene and instruct the pilotto change speed, level off, or change flight trajectory to avoid gettingto close to another aircraft. Thus, in this scenario, the pilot enjoysthe benefit efficient fuel use, flight time, etc. that was planned atthe TOD 12.

Now referring to FIG. 2, another aircraft 24 is now in the local area ofthe first aircraft 2. The second aircraft 24 has its own descent phase26, and accordingly, another set of flight path shadow lines 28 andresulting ground path 30 are provided. As mentioned above, the airportand its ATC may establish a series of waypoints that aircraft musttravel through during the low altitude flight phase 14 of the flighttrajectory. So as the first aircraft 2 and the second aircraft 24 travelthrough their respective descent phases 6, 26 and towards the mergepoint 16, the paths of the two aircraft 2, 24 begin to converge. In someinstances, the distance between two aircraft 2, 24 may become too small,and the two aircraft will have less than the desired safe separation atthe merge point and there is a risk of possible collision. Under theFAA's Order JO 7110.65 Air Traffic Organization Policy (Policy), Section5 stipulates the minimum separation requirements when using radarprocedures to separate aircraft. The minimum separation depends on thetype of radar being used and the distance aircraft are from a singleradar antenna. The minimum separation is typically at least 5 miles whenaircraft are 40 miles or more from the antenna, and aircraft must beseparated by at least 3 miles when aircraft are less than 40 miles fromthe antenna. Section 5 of the Policy has further standards for differenttypes of aircraft, surveillance systems, and other scenarios. Thus, theairport and its ATC must maintain certain distances between aircraft inaccordance with the FAA's 7110.65 Policy.

In FIG. 3, the two aircraft 2, 24 become too close under the FAA'sPolicy as the two aircraft 2, 24 begin their respective descent paths 6,26 toward the merge point 16. Thus, the ATC instructs the first aircraft2 to deviate from its planned descent phase 6 onto a long vector 32,which veers the first aircraft 2 far outside of its intended flighttrajectory. While the ATC's instructions are necessary to comport withthe FAA's Policy, the long vector 32 disrupts the first aircraft pilot'sintended goal when the TOD 12 and the descent segment 6 were planned.For example, the long vector 32 may burn additional fuel when the pilotintended to conserve as much fuel as possible. In another example, thelong vector 32 takes more time to reach the touchdown point 20 when thepilot intended to achieve a faster arrival time when the pilotoriginally planned the TOD 12 and the descent phase 6.

The vast majority of aircraft do not have equipment that receives statevector information from other aircraft in the same area. Instead, pilotssimply plan their TODs and their descent phases ignorant of the airtraffic in the local area, and the pilots subsequently rely on theairport and its ATC system to maintain the requisite distance betweenaircraft. Thus, in most cases, a pilot plans a TOD and a descent phasethat will eventually be in conflict with other aircraft and the FAA'sPolicy before the aircraft actually crosses the TOD and begins thedescent phase.

FIG. 4 shows a flowchart for a Traffic Avoidance Spacing (TAS) system 34that receives broadcasted state vector information from other aircraftin the area, receives information about the instant aircraft, optionallyreceives other relevant information, and then generates a plurality ofpossible flight trajectories. First, the TAS system 34 has a transmitteddata device 36 that accumulates transmitted traffic and airspace datafrom sources external to the instant aircraft. This transmitted data mayinclude data received from Automatic Dependent Surveillance-Broadcast(ADS-B) systems. ADS-B equipped aircraft may broadcast state vectorinformation to other aircraft in the area or to ADS-B stations, whichre-broadcast the information. State vector information may includeinformation about the aircraft's location in space, altitude,climb/descent information, etc.

Additional components of the ADS-B system may be sent to the transmitteddata device 36. For example, Traffic Information Services-Broadcast(TIS-B) provides data on non-ADS-B equipped aircraft to ADS-B equippedaircraft. TIS-B allows ground radar to track non-ADS-B equipped aircraftand then relay that same information to ADS-B equipped aircraft. Anothercomponent of ADS-B is Flight Information Services-Broadcast (FIS-B),which provides National Weather Service reports, temporary flightrestrictions, and other information to equipped aircraft to receiveADS-B.

The TAS system 34 may also comprise an internet-based data device 38which receives supplementary data that does not fit within thetransmitted traffic and airspace data described above. Theinternet-based data device 38 may receive weather reports from theNational Oceanic and Atmospheric Administration, special use airspaceinformation, the intended trajectory of proximate aircraft, windinformation, Airport Surface Detection Equipment runway conflictinformation, Multilateration technology, Nexrad S-Band Doppler weatherradars, etc.

Next, onboard sensors may gather information about the instant aircraft.A local data device 42 may generate state vector information, which caninclude information about the instant aircraft's location in space,altitude, climb/descent information, etc. Further, an air data device 44may gather data regarding airspeed and atmospheric conditions around theinstant aircraft.

An onboard traffic device 40 calculates the state vector information ofthe instant aircraft and the various aircraft in the area. Thetransmitted data device 36, the internet-based data device 38, data fromthe local data device 42, and data from the air data device 44 may becombined and rectified in the onboard traffic device 40. In other words,data from these disparate sources may be combined to formulate a singledata set for the immediate aircraft 2 and other aircraft in the area.For example, state vector information from Source A may be more accuratethan state vector information from Source B. Therefore, the onboardtraffic device 40 records state vector information from Source A unlessSource A is not available, then the onboard traffic device 40 uses statevector information from Source B. This hierarchical knock-out system ofcombining data is only one example. In other embodiments, the data fromthe various sources may be averaged using methods known in the art toderive single sets of data for other aircraft in the area or the instantaircraft. Once the data from the various sources is combined, the datais sent from the onboard traffic device 40 to a trajectory generationdevice 46, which generates a plurality of flight trajectories.

One method for synthesizing flight trajectories is to use point-massequations of motion. With the assumption of flat earth, constantacceleration of gravity, and quasi-steady mass, the resulting point-massequations of motion may include:

V _(t)={(T−D)/m}−g sin γ_(a)  (1)

Ψ_(I)=(g/V _(g))tan φ  (2)

h=V _(t) sin γ_(a) +W _(h)  (3)

x=V _(t) cos γ_(a) sin Ψ_(a) +W _(x)  (4)

y=V _(t) cos γ_(a) cos Ψ_(a) +W _(y)  (5)

s=V _(t) cos γ_(a) +W _(s) =V _(g)  (6)

m=−m _(f)(T,M,h _(p))  (7)

Lift and drag are expressed as:

L=(½)ρ(V _(t))² SC _(L)  (8)

D=(½)ρ(V _(t))² SC _(D),  (9)

Mach number is defined as:

M=(V _(t))/(1.4RΘ)^(1/2)  (10)

In subsonic flight, the calibrated airspeed (CAS) is related to Machnumber, pressure, and temperature through:

V _(CAS)={7RΘ _(SL)({(p/p _(SL))[(0.2M²+1)^(3.5)−]+1}^(2/7)−1)}^(1/2)  (11)

Table I is provided below to identify the various the various constantsand variables in equations 1-11.Table I Summary of constants, coefficients, and variables for thepoint-mass equations.

C_(L), C_(D) (Lift, Drag) coefficient D Aerodynamic drag g Accelerationof gravity h, h_(P) (Geometric, Pressure) altitude L Aerodynamic lift mAircraft mass m_(f) Fuel consumption M Mach number s Path lengthvariable p Pressure p_(SL) Sea-level pressure R Specific gas constant,turn radius S Wing platform reference area T Thrust ν Velocity V_(t)True airspeed V_(CAS) Calibrated airspeed V_(g) Ground speed W_(x),W_(y), W_(h) East, North, Up wind components W_(s) Path length windcomponent x, y East, North coordinate (γ_(a), γ_(I)) (Air-relative,Inertial) flight path angle φ Bank angle ρ Air density (Ψ_(a), Ψ_(I))(Air-relative, Inertial) heading angle measured clockwise from the NorthΘ Outside air temperature at altitude Θ_(SL) Sea-level temperature

A standard avoidance interval (SAI) is described in greater detail belowin FIGS. 5A and 5B and other figures. A SAI is a spacing interval thatis assigned to other aircraft in the area. Thus, the instant aircraftcan set a spacing of greater than 4 miles from the nearest aircraft whenthe FAA's Policy requires only 3 miles of spacing. As a result, theinstant aircraft will most likely not receive a request from an ATC tochange speeds, fly level, or completely deviate from the aircraft'sintended flight trajectory.

Information from the onboard trajectory generation device 46 may includethe established, current flight trajectories but may also include inputsor constraints such as wind information, thunderstorm warninginformation, special use airspace status information, ATC sector andsector loading information, turbulence information, as well as otherhazards to aviation and proprietary information from the airlineoperation control via the internet. However, it will be appreciated thatthe trajectory generation device 46 does not need all of these sourcesto generate a plurality of flight trajectories. For example, in oneembodiment, only the data from the onboard traffic device 40 is used togenerate a plurality of flight trajectories.

However, information regarding the wind at various waypoints may beuseful to avoid weather events such as turbulence or to more effectivelyconserve fuel. The magnitude and directions of wind at a matrix ofwaypoints where wind information is available can be expressed as:

W _(fw)(W _(i) ,h _(j)),ψ_(fw)(W _(i) ,h _(j)),i=1, . . . ,N _(w) ;j=1,. . . ,N _(h)  (12)

where W_(fw) is the forecast wind magnitude, which is a function of windmagnitude W at various altitudes h, and W_(fw) is the forecast winddirection, which is also a function of wind magnitude at variousaltitudes. N_(w) is the number of waypoints at which wind information isavailable, and N_(h) is the number of altitude levels at each waypointwhere wind forecast data is available. A wind interpolation orapproximation scheme can then be used to determine the wind magnitudeand direction at a generic position and altitude.

W _(m)(s,h),ψ_(w)(s,h)  (13)

The East and North wind components W_(x) and W_(y) used in trajectorysynthesis can be determined from:

W _(x) =W _(m) sin ψ_(w) ,W _(y) =W _(m) cos ψ_(w)  (14)

where ψ_(w) is the wind direction measured clockwise from North. Anestimate for the wind at any point synthesized during trajectorygeneration can be found by locating neighboring waypoints where forecastwinds are available, estimating the wind at the current altitude on eachof the neighboring waypoints using vertical interpolation, and thenestimating the wind at the current position and altitude by horizontallyinterpolating the winds between the two neighboring waypoints. Thesensed wind information may be blended with interpolated windinformation to provide the most likely winds at points in the trajectoryahead of the aircraft.

With the requisite information gathered, the trajectory generationdevice 46 may generate a plurality of flight trajectories that areconflict free, which means that the flight trajectories do not cause theinstant aircraft to travel into a SAI of another aircraft, a weatherevent, special use airspace, etc. For some embodiments of the presentinvention the trajectory generation is contemplated to occur onboard theaircraft. However, it will be appreciated that the same calculationscould occur anywhere, provided the relevant data is available.

The generation of flight trajectories may comprise two major components,the generation of the horizontal path and the generation of the verticalpath over the defined horizontal path. As an example, a Dijkstraalgorithm can be used to explore the airspace around the aircraft out tothe destination or to the limit of available information (i.e., thelimit of available surveillance data could be defined as the air-to-airgrange of ADS-B or the limit of surveillance data supplied to the systemvia the internet). The points generated by a Dijkstra algorithm can bedetermined by using a discrete search technique to find a trajectorythat avoids traffic conflicts, special use airspace, avoids hazardousweather, avoids extending over water routing while accounting for ANSPsector boundaries and sector loading. The series of waypoints generatedby the Dijkstra methodology are also subject to aircraft speed and bankangle limitations. Aircraft performance data can be supplied by theaircraft manufacturer or generic values can be looked up on a collectionof American Standard Code for Information Interchange (ASCII) filesequivalent to the Base of Aircraft Data (BADA) maintained byEUROCONTROL.

A Dijkstra algorithm can be used to generate a series of waypoints thatexpands outward from the aircraft's current position or another selectedstarting point, interactively considering every waypoint that requiresoptimization for a parameter (e.g., the least amount of fuel burn orleast amount of time), moving from waypoint to waypoint until thealgorithm reaches the destination or a point where the referencetrajectory can be rejoined.

The Dijkstra methodology determines the next waypoint in a series ofincremental steps to the destination. In the case where the trajectoryis determined onboard the aircraft the position of each “next waypoint”could be limited to waypoints contained within the FMS or limited to allpossible waypoint definable by the fidelity of latitude and longitudecalculations of the FMS.

To determine a range of suitable flight trajectories, a ranked list ofless-than-optimal flight trajectories is found by first determining theoptimal flight trajectory then searching for a flight trajectory withthe optimal solution suppressed. This process is then iterativelyrepeated until the boundaries of the optimized parameter(s) (e.g.,excess fuel burn or elapsed time) are reached. The optimal and rankedsubsequent flight trajectories can be presented for selection by thepilot or the automation.

Just as the Dijkstra methodology is applied to determine the range ofsuitable flight trajectories in the horizontal plane, the same methodscan be applied simultaneously in the vertical plane to generate a4-dimentional trajectory. In addition to using the Dijkstra methodologyto generate a 4-dimentional trajectory, a vertical profile can also beconstructed over the horizontal path determined above. In this case thevertical profile consists of a series of flight segments starting fromthe initial position to runway threshold.

-   The vertical path may be segmented into phases that have different    or changing values for airspeed, Mach, CAS, altitude, aircraft    configuration, flight path angle and thrust. The phases include    climb, cruise, descent to the Mach-CAS transition altitude, constant    CAS descent to a metering fix with a speed constraint or a CAS    descent to the 250 KT deceleration altitude, a deceleration to the    maneuvering speed for intercepting the final approach phase, descent    and decelerating configuration on the final phase. In addition other    variables to the generation of a vertical profile include initial    aircraft conditions, aircraft performance parameters, flight    procedures associated with compliance of ATC regulations and    atmospheric conditions such as turbulence and icing conditions.    Aircraft performance data can be supplied by the aircraft    manufacturer or generic values can be looked up on ASCII tables. The    equations of motion for each of these phases are obtained from the    general point-mass model contained in equations 1 through 11 above.    A first-order Euler integration scheme is then used for the proper    integration with the horizontal path.

The generation of a new vertical path over the existing referencetrajectory flight path during the both descent and climb phases of theflight trajectory present a special case because the vertical path canbe modified by adjusting the speed profile of the aircraft with aconstant thrust setting.

Moving to the next portion of the flowchart in FIG. 4, the plurality offlight trajectories are presented in a display unit 48. A pilot mayreadily thumb through the plurality of flight trajectories and determinewhich flight trajectory best suits the operational requirements of theflight. Therefore, for example, a pilot may select the flight trajectoryfrom an input user interface 50 of the display unit 48 that is going toprovide the most fuel efficient descent phase of a flight, and the pilotknows that there is little or no risk of receiving an intervention by anATC because the system 34 incorporates SAIs. In some embodiments, theairline may have an automated system that, at the input user interface50, selects a flight trajectory from the plurality of flighttrajectories based on one or more parameters. For example, an airlinemay value fast flight times above all else, and thus, the airline wouldhave the automated system select the flight trajectory with the fastestarrival descent time.

Once the selection has been made a FMS 52, or the flight managementdevice, uses the selected flight trajectory to establish a TOD and aspeed profile to have the aircraft 2 travel on the selected flighttrajectory.

FIGS. 5A and 5B depict a second aircraft 24 that has been assigned a SAI54 or a Standard Avoidance Interval. As noted above, an aircraft mayassign a SAI to a second aircraft 24 in the area, and the SAI 54 may bemore conservative than FAA standards such that the aircraft does notincur an intervention by an ATC. Thus, in some embodiments the SAIassigned to another aircraft creates a separation between two aircraftthat is larger than the separation maintained by an ATC under FAA's JO1710.65 standard. As shown in FIG. 5A, the SAI 54 is an area or definedspace that extends in a lateral or horizontal dimension 56 a from thesecond aircraft 24 about a vertical axis, which, in some embodiments,may be positioned over the second aircraft's geometric center or centerof mass.

FIG. 5B shows the SAI 54 extending in a lateral dimension 56 a from thesecond aircraft 24 as well as a vertical separation distance 56 bextending above and below the second aircraft 24. The verticalseparation distance 56 b functions much the same way as the lateraldimension 56 a of the SAI 54. When the TAS system 34 generates aplurality of flight trajectories, the TAS system 34 avoids conflictsbetween the TAS-equipped aircraft and the vertical separation distance56 b of the second aircraft 2. In some embodiments, the verticalseparation distance 56 b may extend 1000 feet above the second aircraft24 and 1000 feet below the second aircraft 24. Further, the verticalseparation distance 56 b may be centered on a geometric center or acenter of mass on the second aircraft 24.

The resulting space surrounding the second aircraft 24 is a threedimensional defined space, and more particularly a cylinder because thelateral dimension 56 a of the SAI 54 is a constant radius from avertical axis and the vertical separation distance 56 b is expressed interms of altitude above and below the second aircraft 24. However, itwill be appreciated that embodiments of the invention are not limited tothese shapes. For example, the SAI 54 may be an ovoid shape thatencompasses a larger area behind the second aircraft 24 to account forwake behind the second aircraft 24. Further, the SAI may be a differentsize and shape during different phases of a flight because the FAA hasdifferent standards during different phases of the flight. For instance,the enclosed volume of the standard avoidance interval may comprise aspheroid shape that is dependent on at least one of the speed,performance, size, configuration and type of aircraft, proximity to anATC boundary or airport, and point in the flight trajectory.

Various entities may establish different standards, sizes, and shapesfor SAIs. A manufacturer, for example of aircraft, may establish a SAIduring certification to avoid conflict with other aircraft. The aircraftoperator and the pilot may also establish various SAIs. In instanceswhere different entities establish different SAIs, an entity may createa more conservative SAI (i.e., larger SAD. In one example, themanufacturer establishes a SAI having a first size, and the airlineoperator establishes a SAI having a second size. The second size islarger and more conservative than the first size. Subsequently, a pilothas the freedom to establish a third SAI that is larger and moreconservative than either the first size or the second size. In otherembodiments, a party with greater authority may wish to overrule anyattempt to establish a larger and more conservative SAI.

FIG. 6 shows an instant aircraft 2 that is equipped with a TAS system 34wherein there are several aircraft 24 in the local area. The TAS system34 has received ADS-B data and state vector information broadcasted fromother aircraft 24 in the area, and the TAS system 34 has assigned a SAIto the position of the other aircraft 24 for the purpose of calculatingconflict-free flight trajectories. It will be appreciated that the TASsystem 34 can assign a different SAI 54 to different aircraft 24depending on several different factors including the size and type ofaircraft 24, the aspects of the aircraft's 24 motion such as velocityand trajectory, the stage of the aircrafts' 2, 24 flights (e.g., descentphase or en route phase), etc.

FIG. 7 shows the geometry of two aircraft traveling toward each otherand the resulting miss distance M_(D) that may be calculated andsubsequently compared to the SAI 54. The TAS system 34 may calculate amiss distance M_(D), or the closest distance that two aircraft will passrelative to each other, based on the state vector information of theinstant aircraft 2 and the second aircraft 24. First, the range r may becalculated with the use of variables a and c, which can be determined byusing the Haversine formula:

a=sin²(Δφ/2)+cos φ1□ cos φ2□ sin²(Δλ/2)  (15)

c=2□a tan 2{(a)^(1/2),(1−a)^(1/2)}  (16)

r=R _(E) c  (17)

where φ is latitude (measured in radians), λ is longitude (measured inradians), RE is earth's radius (mean radius≈6,371 km). Knowing the statevector information of the instant aircraft 2 and the second aircraft 24also enables the determination of bearing β from the instant aircraft 2to the second aircraft 24 using the equation:

β=a tan 2(sin Δλ□ cos φ2,cos φ1□ sin φ2□ sin φ1□ cos φ2□ cos Δλ)  (18)

The relative bearing β′ can be determined by the instant tract anglefrom the position bearing β. The apparent velocity of the secondaircraft 24 can be found by:

v′ ₂₄={(rω)²+ρ²}^(1/2)  (19)

sin φ=(rω)/v′ ₂₄  (20)

M _(D)=(r ²ω)v′ ₇₅₇(r ²ω)/{rω)²+ρ²}^(1/2)  (21)

The TAS system 34 compares the miss distance M_(D) of a flighttrajectory to the SAI 54, and if the miss distance M_(D) is less thanthe SAI, then the flight trajectory has a conflict. The calculationsused to generate the miss distance M_(D) may incorporate the velocity oracceleration of bearing β to account for dynamic flight trajectories.Further, the miss distance M_(D) may incorporate information from localaircraft 24 that indicates where the aircraft 24 is ultimatelytraveling. For example, if the local aircraft 24 is traveling toward amerge point, a way point, or a particular airfield; then thisinformation may be used to predict miss distances M_(D) and potentialfuture conflicts for flight trajectories. Therefore, a known flighttrajectory of a second aircraft may be used to calculate a plurality ofmiss distances using the prescribed SAI along the length of the knownflight trajectory. It will be appreciated that the SAI may change sizeand shape at various points along the known flight trajectory for avariety of factors discussed elsewhere herein. In addition, the knownflight trajectory may include complete flight trajectories and evenincomplete flight trajectories.

FIGS. 8A and 8B depict how variable speed profiles can impact the missdistance between two aircraft relative to a SAI assigned to a secondaircraft. FIG. 8A illustrates three different speed profiles startingfrom the same altitude and measured using a Mach number and a CalibratedAirspeed (CAS). The fastest descent speed results in the shortestlateral distance traveled by the aircraft 2. Conversely, the slowestdescent speed results in the longest lateral distance traveled by theaircraft.

Turning to FIG. 8B, the three speed profiles from FIG. 8A are reorderedsuch that the three speed profiles intersect at the same point behind asecond aircraft 24. Therefore, the instant aircraft 2 can remain atcruising altitude the longest with the fastest speed profile since thefastest speed profile results in the shortest lateral distance traveledby the aircraft 2, and vice versa for the shortest speed profile.Therefore, embodiments of the TAS system 34 may also account fordesirable speed profiles while maintaining the desired distance fromother aircraft 24.

FIG. 9 depicts a TAS equipped aircraft 2 traveling on an en route phase4 of a flight trajectory where another aircraft 24 is in the area, andboth aircraft 2, 24 are traveling toward a merge point 16. Since theinstant aircraft 2 is equipped with a TAS system 34, the pilot selectsamong a plurality of flight trajectories that have a generally lowerspeed profile, which allows the second aircraft 24 to reach the mergepoint first. There are many idle thrust descent speed profiles that willallow the TAS equipped aircraft 2 to avoid a conflict with the secondaircraft 24. This range of idle thrust descent-speed-profiles arebounded by avoiding traffic conflict and the use of operationally soundspeeds. The TAS system has assigned a SAI 54 to the second aircraft 24based on, for example, the type of aircraft, the stage of the flight,and the proximity to an airport and runway 22. The lower speed descentsegment 58 and the associated TOD 60 allow the instant aircraft 2 toachieve a miss distance between the two aircraft 2, 24 that is equal toor greater than the SAI assigned to the second aircraft 24.

By selecting one of the idle thrust descent-speed-profiles from theplurality of descent speed trajectories generated by the TAS the pilotavoids an intervention by an ATC which would cost the pilot even moretime.

It will be appreciated that embodiments of the present invention may beapplied to any phase of the flight including the climb phase, the enroute phase, and the low altitude phase before landing. During the lowaltitude, final approach phase, assignment of a SAI to other proximateaircraft ensures the TAS equipped aircraft does not conflict with eithertraffic ahead of or behind the equipped aircraft while providingguidance to achieve a stabilized approach.

It will be further appreciated that the SAI assigned to other aircraft24 may be different depending on the phase of the flight where the mergeSAI is expected to be achieved. FAA Policy allows for a smaller distancebetween aircraft on approach as opposed to the en route phase of aflight. Accordingly, the TAS on the instant aircraft 2 may set a smallerSAI 54 to the second aircraft 24 for a more fuel efficient, timeefficient, etc. descent while avoiding any intervention by an ATC if thepoint is where the SAI is achieved is on approach as opposed to the enroute phase of a flight.

FIG. 10 shows the situation when safe separation and the associated SAIcan only be achieved by having ATC assign the TAS equipped aircraft 2 avector. While these vectors are undesirable, they may be unavoidable insome instances. In this case the instant TAS equipped aircraft 2 iscoming off of an en route phase 4 and onto a descent phase 58 whereanother aircraft 24 is in the area, and both aircraft 2, 24 aretraveling toward a merge point 16. Since the instant aircraft 2 isequipped with a TAS system 34, The TAS system has assigned a SAI 54 tothe second aircraft 24 based on, for example, the type of aircraft, thestage of the flight, and the proximity to an airport and runway 22. Ifthe geometry of the encounter between aircraft 24 and 2 prevents the TASfrom providing a plurality of operationally sounddescent-speed-schedules, then the TAS will use the SAI to calculate botha new en route 4 cruise speed and a single descent-speed-schedule whichallows the second aircraft 24 to reach the merge point first and reducesthe amount for off path vectoring 62 required by the TAS equippedaircraft 2. Thus, while ATC may extend flight path of the instant TASequipped aircraft 2 by assigning it a short vector the TAS equippedaircraft 2 can reduce the length of the off path vector by providing thepilot with both a new en route 4 cruise speed and adescent-speed-schedule and FMS derived TOD 60 that minimizes the needfor ATC intervention. The new en route 4 speed and lower speed descentsegment 58 and the associated TOD 60 allow the instant aircraft 2 toreduce the amount of ATC intervention. It will be appreciated that theability of the TAS system to propose changes to the flight path indifferent phases, including the en route phase 4, can be applied to anyembodiment described herein.

FIG. 11 shows a TAS equipped aircraft 2 where two other aircraft, asecond aircraft 24 and a third aircraft 64, are in the area around theinstant aircraft 2. Similar to FIG. 9, the second aircraft 24 istraveling on its own descent phase 26 toward a merge point 16. Theinstant aircraft's TAS system has assigned a SAI 54 to the secondaircraft 24 to incorporate the constraint into the TAS system'sgeneration of a plurality of flight trajectories. Also depicted in FIG.11 is a third aircraft 64 that is behind the instant aircraft 2. The TASsystem has assigned a larger SAI 66 to the third aircraft 64 based onvarious aspects of the third aircraft 64. Thus, when the TAS system ofthe instant aircraft 2 generates a plurality of flight trajectories, theTAS system will calculate a miss distances for each aircraft 24, 64 toprovide a plurality of conflict-free flight trajectories that will avoidan intervention by the local ATC.

FIG. 12 illustrates an aircraft 2 that is equipped with a TAS systemwhere there are a second aircraft 24 and a third aircraft 64 in thearea. In this scenario, the second aircraft 24 is traveling toward thesame merge point 16 as the instant aircraft 2. The third aircraft 64 istraveling across the descent phase of the instant aircraft's flighttrajectory at a higher altitude than the instant aircraft 2, but thethird aircraft 64 still presents a conflict to the flight trajectory ofthe instant aircraft 2. Therefore, the TAS system of the instantaircraft 2 may generate a multi-segmented descent phase where eachsegment has a constant speed, and the instant aircraft 2 avoids conflictwith both the second aircraft 24 and the third aircraft 64. The TASsystem may generate a descent phase that comprises a first segment 70and a second segment 74 where the segments are joined at a TrafficAvoidance Waypoint (TAW) 72. The TAW 72 is positioned below the thirdaircraft 64 to avoid conflict with the vertical separation distance ofthe SAI assigned to the third aircraft 64. As a result, the firstsubsegment 70 has a first speed profile, and the second subsegment 74has a second speed profile where the first speed is faster than thesecond speed. This multi-segment approach allows a TAS equipped aircraftto handle crossing aircraft in addition to the embodiment described inFIG. 11, where the third aircraft 64 is generally behind the instantaircraft 2 and traveling on a similar flight trajectory as the instantaircraft 2.

A plurality of TAWs may be generated, which provides a pilot of a TASequipped aircraft with a number of options. Similar to the embodimentsdescribed in FIGS. 9-11, a pilot may select the particular TAW that bestsuits the preferences of the pilot, the airline, or any other entity.Then, an updated TOD 68 is calculated, and the new flight trajectoryinformation is supplied to a Vertical Navigation (VNAV) system. The TAWcrossing restriction may be a dynamically assigned waypoint thatmodifies the VNAV profile. The TAW may not make part of the VNAV pathuntil the actual encounter geometries of proximate traffic are known.The TAW may be determined through the generation of the plurality offlight trajectories and may be entered into the FMS prior to the TOD.

During the descent phase of a flight, the ground path is generallyfixed, and a plurality of TAWs may be provided at various altitudesabove a reference point on the ground path. This reference point abovethe ground path may be selected by first identifying a miss point on theoriginally-planned flight trajectory that has the smallest miss distancewith respect to the third aircraft 64. The ground path below this misspoint on the originally-planned flight trajectory may then be used as areference to provide a plurality of TAWs at various altitudes.

Other pluralities of TAWs may be provided in a two dimensional area or athree dimensional volume instead of a plurality of TAWs in just onedimension. In an exemplary embodiment, a plurality of TAWs is generatedat various altitudes along a length of the ground path. Yet it will beappreciated that a two dimensional area of TAWs may not be positionedover the ground path. Further, in another exemplary embodiment, aplurality of TAWs is generated at various altitudes both on and off ofthe ground path to define a three dimensional volume. Further yet, atime component may be added to any of the TAWs as one or both of theinstant aircraft 2 and the third aircraft 64 change trajectories and themiss distance between the two aircraft 2, 64 changes over time. It willbe appreciated that miss distance between two aircraft may not be theonly basis to calculate a plurality of TAWs. For example, TAWs may beestablished at a midpoint between an originally-planned TOD 68 and amerge point 16.

Next, limits 76, 78 may be established to remove TAWs that would createa flight trajectory with a conflict, for example, a conflict with a SAIassigned to another aircraft. A plurality of TAWs may be bound by anupper altitude limit 76 and/or a lower altitude limit 78. These limits76, 78 may also be expressed in terms of other parameters such asairspeed. Thus, with the embodiment shown in FIG. 12, pilot may select aTAW 72, and the aircraft 2 may pass at or above a lower altitude limit78 and at or below an upper altitude limit 76. In other embodiments, theaircraft 2 may pass at or above a lower limit 78 at a specific airspeedand at or below an upper limit 78; at or above a lower limit 78 at aspecific airspeed and at or below an upper limit 78 at a specificairspeed; or at or above a lower limit 78 and below an upper limit 78 ata specific airspeed. In other embodiments, only one limit exists and inyet other embodiments, the two limits converge and the aircraft mustcross at a specific altitude and/or airspeed to avoid having a conflict.

Since the third aircraft 64 in FIG. 12 is crossing at a higher altitude,the upper altitude limit 76 of the TAW 72 may be established by a SAI ora vertical separation distance assigned to the third aircraft 64. Incontrast, the lower altitude limit 78 may be established by operationallimitations of the instant aircraft 2 such as maximum time allowed,maximum fuel allowed, or any other parameter discussed elsewhere herein.Then the pilot or automated system may choose a TAW 72 that best suitsthe needs of the particular airline, flight, or any other parameter.

The embodiment in FIG. 13 shows a flight trajectory and a descent phasethat comprises two segments 80, 84 joined together at a TAW 82. However,in the embodiment shown in FIG. 13, the third aircraft 64 is crossing ata lower altitude. Therefore, the TAW 82 is positioned such that thefirst segment 80 has a lower speed than the second segment 84. Again,the two segments generated by the TAS system may not be as efficient interms or fuel or time as a single speed subsegment. But the TAS systemenables the instant aircraft 2 to avoid interventions by an ATC, whichwould cost the instant aircraft 2 even more fuel and time. Similar tothe embodiment in FIG. 12, the TAW 82 in FIG. 13 may be selected betweenan upper limit 86 and a lower limit 88.

FIG. 14 depicts a TAS equipped aircraft 2 with a speed profile thatfollows a brachistochronic curve, which has a variable speed profile andresults in a rapid descent phase 90 that saves energy and reduces theneed for intervention by the ATC. In this embodiment, the pilot ispresented with a plurality of TAWs 92 having an upper limit 94 and alower limit 96. The selected TAW 92 is a point in space, and the pilothas chosen a brachistochronic speed profile that passes through theselected TAW 92 and avoids a conflict with a third aircraft 64. Theflight trajectories illustrated in FIGS. 12 and 13 have multi-segmentedprofiles joined together at a TAW. However, flight trajectories may begenerated that pass through the TAW and have a continuously variablespeed profile. A brachistochronic curve is the path of shortest possibletime for a aircraft to descend from a given point to another point thatis not directly below the start where the only external force is gravityand the velocity at which the aircraft travels at is not constant.

The parametric expression of a brachistochronic speed profile can becharacterized by:

x=r(θ−sin θ);y=r(1−cos θ)  (22)

The TAS system enables descents with continuously changing velocity suchas a brachistochronic or cycloidal trajectory descent between the TOD 68to the merge point 16 through a selected TAW.

In further embodiments of the invention, additional types of waypointsmay be utilized alone or in combination with TAWs. For example, anenergy management waypoint (EMW) may be used to guide a flighttrajectory and an aircraft through a waypoint that ensures avoidance oficing conditions, safe approaches and landings, avoidance of turbulence,etc.

Icing conditions may be defined as an icing event such as a supercooledcloud where the icing event defines a volume, and at least a portion ofthe volume has a temperature between approximately −5° C. and 2° C.Under these conditions, supercooled droplets of water or ice may impactthe leading edge of a body on the aircraft then freeze or refreeze oncooler trailing edges of the body. Accretions of ice can alter thegeometry of the aircraft, alter instrument readings, and add weight tothe aircraft, all of which can jeopardize the safety of the aircraft.Additional information regarding the Federal Aviation Administration'scharacterization of icing events may be found in Advisory Circular No.91-74A, entitled Pilot Guide: Flight in Icing Conditions and dated Dec.31, 2007.

Turbulence comprises several features of airflow including irregularity,diffusivity, rotationality, and dissipation. Turbulent airflow can causepassenger discomfort when these feature of airflow become too erratic orchaotic. Airflow is conventionally divided into laminar flow andturbulent flow, and the Reynolds Number is frequently used todistinguish between these two types of flow. The equation for theReynolds Number is defined as

$\begin{matrix}\frac{\rho \; {vL}}{\mu} & (23)\end{matrix}$

where ρ is the density of the fluid (in this case air), v is the maximumvelocity of an object (aircraft) relative to the fluid, L is thecharacteristic linear dimension of the object, and μ is the dynamicviscosity of the fluid. Essentially, the Reynolds Number is the ratio ofinertial forces over viscous forces, and when the inertial forces aremuch larger than the viscous forces, then the fluid is turbulent. Inmost cases, a Reynolds Number greater than 5000 indicates a turbulentfluid.

In various embodiments, the EMW is generated to avoid the turbulentevent or the icing event. However in other embodiments, an EMW may begenerated to provide a range of acceptable airspeeds in a turbulentevent or an icing event. Therefore, if it is unfeasible to completelyavoid, for example, a turbulent event, then a range of airspeeds may beassigned to an EMW, or each EMW in a plurality of EMWs, to increasepassenger comfort, safety, etc.

EMWs may be generated alone or in combination with TAWs. For example,after a plurality of TAWs is determined, then EMWs may be determinedfrom the plurality of TAWs, and EMWs form a subset of the TAWs. As aresult, the selected waypoint would be both a TAW and an EMW.Conversely, a plurality of EMWs may be determined that are wholly orpartially different than the plurality of TAWs. In these embodiments, itmay be possible for a selected TAW and a selected EMW to be distinct,and the flight trajectory passes through both selected waypoints.

FIGS. 9-14 focus on implementation of embodiments of the presentinvention to a vertical path of the aircraft. However, embodiments ofthe present invention may also be applied to a lateral path of theaircraft. Then accordingly, embodiments of the present invention may beapplied to all three physical dimensions and a time dimension (4D).

FIG. 15 shows a top view of an aircraft traveling on a selected flighttrajectory 98 among several available airways 100, or establishedcorridors for aircraft to travel in. Wind information regarding thelocal wind field 102 is included in the TAS system's generation of aplurality of flight trajectories. As with other parameters, the TASsystem may include the wind field information to optimize a flighttrajectory for parameters such as fuel conservation or time efficiency.

FIG. 16 illustrates a TAS equipped aircraft 2 traveling along a selectedflight trajectory 98 with other aircraft 24, 64 traveling in the area.However, several weather events 104 are also located in the area, and aconflict weather event 106 is located on the selected flight trajectory98. A weather event may include thunderstorms, microbursts, generalturbulence, or any other atmospheric effect that may be undesirable dueto safety, passenger comfort, time and fuel efficiency, etc. Thus, theTAS system may assign a SAI to a conflict weather event 106 like the TASsystem assigns a SAI to another aircraft. The TAS system generates aplurality of flight trajectories that are conflict-free and do not bringthe aircraft 2 too close to the conflict weather event 106. In thisembodiment, the TAS system has generated two flight trajectories. Afirst flight trajectory 108 is optimized for the least time to anairport or a waypoint, and a second flight trajectory 110 is optimizedfor the least amount of fuel consumed to avoid the conflict weatherevent 106.

Both trajectories 108, 110 pass along the downwind side of the conflictweather event 106, and the SAI may require adjustment. Passing on thedownwind side of a weather event may expose the aircraft, passengers,cargo and crew to turbulence and hail that can be ejected from theweather event. The TAS system allows for the dynamic adjustment of theSAI assigned to the conflict weather event 106 such that the aircraft 2must pass by the downwind side of the conflict weather event 106 by awider margin. Thus, the more fuel efficient or time efficient trajectorymay be on the upwind side of the conflict weather event 106 to avoid thepossibility of undue turbulence or being subject to hail.

FIG. 17 illustrates a TAS equipped aircraft 2 where the TAS systemgenerates a plurality of flight trajectories based on a range ofparameters. A first flight trajectory 108 and a second flight trajectory110 represent flight trajectories that are optimized for time efficiencyand fuel efficiency, respectively. The TAS system also accounts formaximum fuel burn allowable and maximum time allowable values for thefuel and time parameters. Using the time parameter as an example, afterthe first flight trajectory 108 is calculated, a second solution isgenerated where the second solution is not the optimal solution fortime. In other words, the optimal solution is suppressed during the nextflight trajectory generation or determination. This process isiteratively repeated until a flight trajectory is calculated with themaximum time allowed. As a result, a plurality of flight trajectories isgenerated that ranges in time value between the most time optimum flighttrajectory and the flight trajectory that uses the most time allowed.When combined with the plurality of flight trajectories based on fuel,lateral boundaries 112, 114 are established that define the extent ofthe acceptable flight trajectories.

Also shown in FIG. 17 is the shading of the plurality of flighttrajectories. Some flight trajectories in the plurality of flighttrajectories may be time efficient but fuel inefficient. In contrast,some flight trajectories may be fuel efficient but time inefficient.Further yet, some flight trajectories may be both fuel and timeefficient or both fuel and time inefficient. Without additionalinformation, a pilot may not be able to discern these differences.Therefore, a ranking system may be provided in some embodiments of theinvention.

Since the flight trajectories are iteratively calculated starting withthe most optimized solution for a given parameter and ending with theleast optimized solution, a number may be assigned to each solution. Forexample, “1” may be assigned to the most optimized solution, “2” to thesecond most optimized solution, etc. With multiple parameters, a givenflight trajectory may have a “1” for fuel efficiency and a “5” for timeefficiency. With equal weighting, this flight trajectory would have anaverage score of “3”. To help visualize the results of this grading on adisplay unit, the highest scores (i.e., lowest numbers) could beassigned a color with a higher brightness value or luminosity and thelowest scores could be assigned the same color with a lower brightnessvalue or luminosity. Then, a pilot may better select a flight trajectoryamong a plurality of flight trajectories.

FIG. 18 depicts a TAS equipped aircraft 2 that has generated a pluralityof flight trajectories 116 off of the Gulf Coast of Florida. Thisplurality of flight trajectories 116 presents trajectories that rangethrough parameter values as described in reference to the embodiment ofFIG. 17. The plurality of conflict-free flight trajectories 116 in FIG.18 account for local weather events 104 and an Airline OperationalControl (AOC) requirement that the aircraft cannot fly more than a setdistance from shore.

FIG. 19 depicts the relationship between different speed profiles duringthe descent phase of a flight trajectory. When an aircraft is flown atslower speeds the aircraft's descent is shallower than when the aircraftflies at higher speeds, provided the throttle is at idle and theaircraft is in the same configuration. The optimum descent speed profile118 predicated on the FMS idle thrust, descent speed schedule using thecost index associated with the filed flight plan and does not accountfor conflicting traffic, inclement weather, or changes in operationalrequirements to speed up or slow down to meet schedule. Theoperationally high speed profile 120 represents the fastest idle thrust,speed profile the aircraft should fly. The operationally low speedprofile 122 represents the slowest idle thrust, speed profile theaircraft should fly. The aircraft limit lines 124 and 126 represent thespeed profiles associated with the airframe limits. The fastest descentspeed schedule 128 that avoids conflict with leading traffic or trafficthat is ahead of the equipped aircraft may, at times, be greater thatthe operationally high speed limit 120 and the aircraft limit 124. Thefastest descent speed to avoid conflicts with other proximate trafficmay also be less than the speed schedule associated with the optimumspeed schedule 118. This variation of the high speed descent speedprofile is represented by the double headed arrow 132. The slowestdescent speed schedule 58 that avoids conflict with training traffic ortraffic that is behind of the equipped aircraft may, at times, be lessthan the operationally sound low speed limit 122 and the aircraft limit126. The slowest descent speed 130 to avoid conflicts with otherproximate traffic may also be greater than the speed schedule associatedwith the optimum speed schedule 118. This variation of the descent speedprofile 130 is represented by the double headed arrow 134.

While the above description and drawings disclose and illustrateembodiments of the invention, it should be understood that the inventionis not limited to these embodiments. It will be appreciated that theadjustment of en route 4 speeds can be adjusted by the instant aircraftequipped with TAS 34. It will be further appreciated that othermodifications and changes employing the principles of the invention,particularly considering the foregoing teachings, may be made.Therefore, by the appended claims, the applicant intends to cover suchmodifications and other embodiments.

What is claimed is:
 1. A method for automatically determining aplurality of conflict-free flight trajectories for a first aircraft,comprising: providing a traffic avoidance spacing system having at leastone electronic device to process instructions for determining aplurality of flight trajectories and providing a flight managementsystem; providing information regarding a first aircraft moving in spaceaccording to a first state vector; providing information regarding asecond aircraft moving in space according to a second state vector, saidsecond aircraft having a standard avoidance interval extending in atleast one direction from said second aircraft; providing sector loadinginformation regarding a number of aircraft in an air traffic controlsector; determining, by said at least one electronic device, a firstflight trajectory for said first aircraft based on said first statevector of said first aircraft and based on said sector loadinginformation; comparing, by said at least one electronic device, saidfirst flight trajectory to said second state vector of said secondaircraft to determine a miss distance between said first aircraft andsaid second aircraft; comparing, by said at least one electronic device,said miss distance to said standard avoidance interval of said secondaircraft to confirm that said miss distance is greater than saidstandard avoidance interval; determining, by said at least oneelectronic device, a second flight trajectory for said first aircraftbased on said first state vector of said first aircraft and based onsaid sector loading information, said second flight trajectory beingdistinct from said first flight trajectory; and receiving and executing,by said flight management system, one of said first and second flighttrajectories so that said first aircraft travels on a conflict-freeflight trajectory.
 2. The method of claim 1, further comprising:comparing, by said at least one electronic device, said second flighttrajectory to said second state vector of said second aircraft todetermine a second miss distance between said first aircraft and saidsecond aircraft; and comparing, by said at least one electronic device,said second miss distance to said standard avoidance interval of saidsecond aircraft to confirm that said second miss distance is greaterthan said standard avoidance interval.
 3. The method of claim 1,wherein: said first flight trajectory is optimized for a parameter. 4.The method of claim 3, wherein: said parameter is fuel efficiency,wherein a plurality of first flight trajectories range between saidfirst flight trajectory and a first flight trajectory that uses amaximum fuel allowance, and wherein said flight management systemreceives and executes a flight trajectory from one of said plurality offirst flight trajectories and said second flight trajectory so that saidfirst aircraft travels on a conflict-free flight trajectory.
 5. Themethod of claim 3, wherein: said parameter is time efficiency, wherein aplurality of first flight trajectories range between said first flighttrajectory and a first flight trajectory that uses a maximum timeallowance, and wherein said flight management system receives andexecutes a flight trajectory from one of said plurality of first flighttrajectories and said second flight trajectory so that said firstaircraft travels on a conflict-free flight trajectory.
 6. The method ofclaim 1, wherein: said standard avoidance interval defines an enclosedvolume surrounding said second aircraft, and said enclosed volume has acylindrical shape, said top and bottom surfaces of said enclosed volumedefined by a vertical separation distance, and said circumferentialsurface of said enclosed volume defined by a radial distance.
 7. Themethod of claim 1, further comprising: providing information regardingan upper air speed and a lower air speed below a Mach-CAS transitionaltitude; and comparing, by said at least one electronic device, a speedprofile of said first flight trajectory to said upper air speed and saidlower air speed to confirm that said speed profile of said first flighttrajectory is less than said upper air speed and greater than said lowerair speed when said first aircraft is below said Mach-CAS transitionaltitude.
 8. A method for minimizing an off-path vector for a firstaircraft, comprising: providing a traffic avoidance spacing systemhaving at least one electronic device to process instructions fordetermining a plurality of flight trajectories and providing a flightmanagement system; providing information regarding a first aircraftmoving in space according to a first state vector; providing informationregarding a second aircraft moving in space according to a second statevector, said second aircraft having a standard avoidance intervalextending in at least one direction from said second aircraft;determining, by said at least one electronic device, a plurality offlight trajectories for said first aircraft based on said first statevector of said first aircraft; comparing, by said at least oneelectronic device, said flight trajectories to said second state vectorof said second aircraft to determine a plurality of miss distancesbetween said first aircraft and said second aircraft; selecting, by apilot of said first aircraft, a flight trajectory from said plurality offlight trajectories based on said miss distance for said selected flighttrajectory to minimize an off-path vector for said first aircraft andbased on a parameter; receiving and executing, by said flight managementsystem, said selected flight trajectory; and receiving and executing, bysaid flight management system, an off-path vector from an air trafficcontrol.
 9. The method of claim 8, wherein: said parameter is fuelefficiency, wherein said plurality of flight trajectories range betweena flight trajectory that uses a minimum fuel allowance and a flighttrajectory that uses a maximum fuel allowance.
 10. The method of claim8, wherein: said parameter is time efficiency, wherein said plurality offlight trajectories range between a flight trajectory that uses aminimum time allowance and a flight trajectory that uses a maximum timeallowance.
 11. The method of claim 8, further comprising: determining,by said at least one electronic device, a plurality of second flighttrajectories for said first aircraft based on said first state vector ofsaid first aircraft, said second flight trajectories being distinct fromsaid flight trajectories; and comparing, by said at least one electronicdevice, said second flight trajectories to said second state vector ofsaid second aircraft to determine a plurality of second miss distancesbetween said first aircraft and said second aircraft; and selecting, bysaid pilot of said first aircraft, a flight trajectory from saidplurality of flight trajectories and said plurality of said secondflight trajectories based on said miss distance for said selected flighttrajectory to minimize said off-path vector for said first aircraft andbased on said parameter.
 12. The method of claim 8, wherein: saidstandard avoidance interval defines an enclosed volume surrounding saidsecond aircraft, and said enclosed volume has a cylindrical shape, saidtop and bottom surfaces of said enclosed volume defined by a verticalseparation distance, and said circumferential surface of said enclosedvolume defined by a radial distance.
 13. The method of claim 8, furthercomprising: providing information regarding an upper air speed and alower air speed below a Mach-CAS transition altitude; and comparing, bysaid at least one electronic device, speed profiles of said plurality offlight trajectories to said upper air speed and said lower air speed toconfirm that speed profiles of said flight trajectories are less thansaid upper air speed and greater than said lower air speed when saidfirst aircraft is below said Mach-CAS transition altitude.
 14. Themethod of claim 8, wherein: said flight trajectories of said pluralityof flight trajectories each include a first segment wherein said firstaircraft has a first speed profile and a second segment wherein saidfirst aircraft has a second speed profile, wherein said first speedprofile and said second speed profile are distinct.
 15. The method ofclaim 1, further comprising: comparing, by said at least one electronicdevice, said plurality of flight trajectories to a weather event toconfirm said plurality of flight trajectories does not conflict withsaid weather event.
 16. A system for automatically determining aplurality of conflict-free trajectories for a first aircraft,comprising: a local data device that determines a first state vector fora first aircraft, said local data device sends said first state vectorfor said first aircraft to a trajectory generation device; a transmitteddata device that determines a second state vector for a second aircraft,said transmitted data device sends said second state vector for saidsecond aircraft to said trajectory generation device; said trajectorygeneration device assigns a standard avoidance interval to said secondaircraft, said standard avoidance interval extends in at least onedirection from said second aircraft, said trajectory generation devicedetermines a plurality of flight trajectories based on said first statevector of said first aircraft and based on sector loading informationregarding a number of aircraft in an air traffic control sector, saidtrajectory generation device compares each flight trajectory to saidsecond state vector of said second aircraft to determine a plurality ofmiss distances, said trajectory generation device confirms that eachmiss distance is greater than said standard avoidance interval for saidsecond aircraft; an input user interface operably interconnected to saidtrajectory generation device and a flight management system, said inputuser interface configured to receive an input from a pilot of said firstaircraft to select a conflict-free fight trajectory from said pluralityof conflict-free flight trajectories, said input user interface sendssaid selected conflict-free flight trajectory to said flight managementsystem; and said flight management system receives and executes saidselected conflict-free flight trajectory from said plurality ofconflict-free flight trajectories so that said first aircraft travels onsaid received conflict-free flight trajectory.
 17. The system of claim16, further comprising: a display unit operably interconnected to saidtrajectory generation device, said display unit displays said pluralityof conflict-free flight trajectories.
 18. The system of claim 16,further comprising: an onboard traffic device that is operablyinterconnected to said transmitted data device and said trajectorygeneration device; an internet-based data device that determines anotherstate vector for said second aircraft, wherein said onboard trafficdevice synthesizes said state vector for said second aircraft from bothsaid transmitted data device and said internet-based data device, andsends said synthesized state vector for said second aircraft to saidtrajectory generation device.
 19. The system of claim 16, furthercomprising: an air data device that determines at least one of airspeeddata and atmospheric data surrounding said first aircraft, and said airdata device sends said data to said trajectory generation device. 20.The system of claim 19, wherein: said air data device sends dataregarding a weather event having a volume to said trajectory generationdevice, wherein said trajectory device confirms that each flighttrajectory avoids said volume of said weather event.